Exponential Decay Calculator Formula

Understand the math behind the exponential decay calculator. Each variable explained with a worked example.

Use the Exponential Decay Calculator

Formulas Used

Remaining

remaining = initial * pow(1 - decay_rate / 100, periods)

Lost

lost = initial - initial * pow(1 - decay_rate / 100, periods)

Pct Remaining

pct_remaining = pow(1 - decay_rate / 100, periods) * 100

Half Life

half_life = decay_rate > 0 ? log(0.5) / log(1 - decay_rate / 100) : 0

Variables

VariableDescriptionDefault
initialInitial Value1000
decay_rateDecay Rate (%)(%)10
periodsNumber of Periods5

How It Works

Exponential Decay

Formula

Remaining = Initial × (1 - r)^t

where r is the decay rate per period and t is the number of periods.

Half-Life

The time for the quantity to reduce to half:

t½ = ln(0.5) / ln(1 - r)

Worked Example

1000 decaying at 10% per period for 5 periods.

initial = 1000decay_rate = 10periods = 5
  1. 01Remaining = 1000 × (0.90)^5
  2. 02= 1000 × 0.59049
  3. 03= 590.49
  4. 04Amount lost = 409.51
  5. 05Half-life = ln(0.5)/ln(0.90) ≈ 6.58 periods

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